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The phrase "the minimum necessary" is correct and usable in written English.
It is generally used to indicate the smallest amount of something needed to accomplish something. For example, "We need to take the minimum necessary steps to complete this project on time."
Exact(60)
Give the Palestinians only the minimum necessary".
Any restrictions must be the minimum necessary.
He withdrew only the minimum necessary.
But the ACP governments yesterday insisted that €250m was the minimum necessary.
He'd always chosen the minimum necessary, a bare-bones, high-deductible plan.
Health plans must limit any disclosures to the minimum necessary for the approved purpose.
We should be proud of them and the British tradition of using the minimum necessary force".
"The proceedings Microsoft has proposed are the minimum necessary to achieve that objective," the company added.
Proportional means: Is the force proposed the minimum necessary to meet the threat?
Or we could continue doing the minimum necessary to avoid losing.
This was, the definition stated, distinguishable from most computer users, who "prefer to learn only the minimum necessary".
More suggestions(15)
the minimum prior
the required necessary
the less necessary
the minimum exists
the minimum demands
the minimum appropriate
the components necessary
the minimum essential
the requirements necessary
the minimum needed
the minimum requirements
the very minimum
the minimal necessary
the lowest necessary
the smallest necessary
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com